{"paper":{"title":"Greedy vector quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gilles Pag\\`es, Harald Luschgy","submitted_at":"2014-09-02T14:41:18Z","abstract_excerpt":"We investigate the greedy version of the $L^p$-optimal vector quantization problem for an $\\mathbb{R}^d$-valued random vector $X\\!\\in L^p$. We show the existence of a sequence $(a_N)_{N\\ge 1}$ such that $a_N$ minimizes $a\\mapsto\\big \\|\\min_{1\\le i\\le N-1}|X-a_i|\\wedge |X-a|\\big\\|_{L^p}$ ($L^p$-mean quantization error at level $N$ induced by $(a_1,\\ldots,a_{N-1},a)$). We show that this sequence produces $L^p$-rate optimal $N$-tuples $a^{(N)}=(a_1,\\ldots,a_{_N})$ ($i.e.$ the $L^p$-mean quantization error at level $N$ induced by $a^{(N)}$ goes to $0$ at rate $N^{-\\frac 1d}$). Greedy optimal seque"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0732","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}